active h∞ control of the vibration of an axially moving cantilever beam by magnetic force

an h_∞ method for the vibration control of an iron cantilever beam with axial velocity using the noncontact force by permanent magnets is proposed in the paper. the transverse vibration equation of the axially moving cantilever beam with a tip mass is derived by d'alembert's principle and then updated by experiments. an experimental platform and a magnetic control system are introduced. the properties of the force between the magnet and the beam have been determined by theoretic analysis and tests. the h_∞ control strategy for the suppression of the beam transverse vibration by initial deformation excitations is put forward. the control method can be used for the beam with constant length or varying length. numerical simulation and actual experiments are implemented. the results show that the control method is effective and the simulations fit well with the experiments.